Simple meshing and efficient numerical analysis of curved surfaces using a new quadrilateral basis function

In this paper, a quadrilateral roof-top type of basis function is presented. Four arbitrary and not necessarily coplanar points establish the associated curved basis function surface. In addition to this, the defined current density is conveniently decomposed into sinusoidally excited strips, vastly reducing the computation time required to determine the associated near zone-field. Moderately curved geometries can be easily meshed by projecting a rectangular grid unto the surface, while fulfilling the objective of quasi-orthogonal current densities on each basis function. To demonstrate the capabilities of the proposed basis function, a case study is presented where the current density induced on the curved surface of a paraboloid is determined using the method of moments. The corresponding results are shown to agree very well with the known correct solution.